Fig. 1. Diagram of three-step model^[11]

Fig. 2. Experimental scheme of HHG with two-color counter-rotating circularly-polarized laser pulses^[13]. Two pump pulses with central wavelengths around 790 nm (LCP, 1.6 mJ/pulse) and 395 nm (RCP, 0.43 mJ/pulse) are focused into a gas-filled hollow fiber

Fig. 3. Spectra of circularly-polarized extreme ultraviolet and soft X-ray HHG^[32]

Fig. 4. Quantum trajectories and angular momentum transfer of electrons^[38]

Fig. 5. Diagram of generating extreme ultraviolet HHG with OAM by focusing two non-collinear beams. (a) Two-color laser field simulation^[14]. An 800 nm Gaussian beam with peak intensity of ${\mathrm{10}}^{\mathrm{14}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$ and a 400 nm vortex beam ($l=\mathrm{1}$) with peak intensity of ${\mathrm{10}}^{\mathrm{13}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$ are focused into argon jet at an angle of $\mathrm{2}.{\mathrm{3}}^{\circ }$; (b) experimental scheme^[43]. Two linearly-polarized beams (800 nm), where one is a Gaussian beam with peak intensity of $\mathrm{2}\times {\mathrm{10}}^{\mathrm{14}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$ and the other is a vortex beam ($l=\mathrm{1}$) with peak intensity of $\mathrm{2}\times {\mathrm{10}}^{\mathrm{12}}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$, are focused into argon jet at an angle of 40 mrad

Fig. 6. Experimental scheme for generating HHG with self-torque^[46]. Two linearly-polarized vortex beams (800 nm) with different topological charges ($l=\mathrm{1}$ and $l=\mathrm{2}$) are focused into gas jet. Their pulse widths and relative time delays are 10 fs

Fig. 7. Simulation results^[22]. (a) HHG spectrum driven by two-color reverse vortex STOV fields; (b) HHG spectrum driven by two-color reverse spin and reverse vortex STOV fields

Fig. 8. Polarization states of torus-knot beams in cross section^[59]. Numbers $\left(m_{\mathrm{1}},m_{\mathrm{2}}\right)$ in upper left of each panel are topological charges of ω and 2ω components, and numbers in upper right of each panel are corresponding parameters $\gamma$

Fig. 9. HHG characteristics in case of conservation of torus-knot angular momentum. (a) HHG spectrum driven by two-color reverse spin vortex fields with $l_{\mathrm{1}}=l_{\mathrm{2}}=\mathrm{1}$^[60]; (b) experimental scheme for generation of spatially separated attosecond pulses^[61]. Two vortex beams with central wavelengths around 785 nm (LCP) and 392 nm (RCP) are focused into gas jet, and their topological charges are adjusted by replacing corresponding spiral phase plates independently